The implementation of Hamiltonian algebrization and Kovacic's algorithm reaches a considerable power in the realm of supersymmetric quantum mechanics. In fact the integrability of second-order linear equations like the radial Schrödinger equation (REF ) subject of our study, via the Kovacic's algorithm is deeply related with the properties of the solutions of the associated Riccati equation in the supersymmetric extension of the theory [1]}. Taking this as a motivation, we go further in this section and propose a superpotential leading to the non-effective part (REF ) of () (\(C=0\) ) as one of two partner potentials. If we denote the superpotential in one dimension as \(w(r) \)  the corresponding partner potentials are given by equation (REF ) (see [1]}, [3]}, [4]}, among others)
\(v_{\pm }(r) \equiv w^{2}(r) \pm \frac{{\rm d}w}{{\rm d}r}\) 
